9. Physics | Dispersion of Light | Aberrations in Lenses and Mirrors | by Ashish Arora (GA)


now we will study aberrations in lensses and
mirrors , here we can write – defects, of images. formed by , lensses and mirrors, are
called. aberrations . and , these are classified- we are talking about aberrations these are
classified . in 2 main categories. these are- we will study one by one these 2, first one
is . chromatic aberrations. and about chromatic aberrations we can write
– these are defects , obviously defects in images formed, due to , dispersion of light.
by a lens. because of which image is being produced or images are being produced if more
than one wavelength is there in light , more than one images will be produced , and here
we can write as – mirrors do not exhibit the characteristic of dispersion so mirrors are
free from chromatic aberrations . here we can also write that – all kinds of
mirrors are free, from , chromatic. aberrations, let’s consider the aberrations in lens , if
we talk about a convex lens – about convex lens we can write that its focal length is
given by lens makers formula given as- 1 by f is equal to mu minus 1 – 1 by r1 minus
1 by r2 . here we can see that – if refractive index
increases- the focal length of the lens decreases, when a white light is allowed to incident
on the lens , parallel to principal axis – then we know well that- mu – of violet light is
refractive index , of lens for violet light is greater than refractive index for red light
, we can write that focal length of lens for violet light is less than the focal length
of lens for red light . so in this situation when white light is incident
on to it – all violet color rays, will focus at a point which we can write as – focal
length for violet color , and similarly all red rays will split from the original beam
and these will . incident – or focus at a point which we can write as- focus point for
red light and this was the focus point for the violet light and the distance of this
point – from the lens would be f-r . and these fv and fr can be calculate using
lens makers formula by using refractive index for violet and red light, so here we can see,
even when a single white light beam is incident on to the lens, several colored focal points
will be obtained on the other side of the lens , similarly if we produce the image of
an object which is white in color or emitting white light- by lens- there are several images
produced , here we can see a realistic situation in which we can see for a convex lens- if
a white object is placed a source of light is placed it produces.
images on the other side which are spreaded between violet image and red image this is
because of dispersion of light through the lens -and we can say lens behaves like a combination
of several lensses with several focal lengths each for an individual wavelength , this is
, the defect of image formation due to various colors in incident light and this is what
we call chromatic aberrations, let’s continue with the second category .
let us continue our discussion for the second category of aberrations which we call – spherical
aberration. about spherical aberrations we can write – these are . defects in images.
due to large aperture. of- lensses, or mirrors. this is because if we consider – a lens, we
have already studied that all light rays which are paraxial incident on to the lens will
focus, at a point which we call its focus- and all rays which are not paraxial rays which
are also called marginal rays . the rays which are very close to principal
axis we call these rays –we have already studied that -these are called , paraxial
rays, and the rays which are – away from principal axis are called , marginal rays. so these
marginal rays, due to, the radius of curvature of lens – after refraction from the 2 surfaces
of the lens will converge at a point , which is closer to focus – this is the reason why
. lens formula or mirror formula is only valid for paraxial rays .
if light rays are incident on to the lens or mirror which are away from principal axis
, or marginal rays- will not converge at focal point similarly when for an object image is
not produced at a single point it will be blurred or distributed between- few points
if we consider marginal rays are originated from the object .
similar to this if we talk about, concave mirror the same phenomenon we can explain
– like parallel incidence rays are incident on concave mirror which are paraxial , after
reflection these light ray will- converge to a point which we term as focus – but
if we consider marginal rays- on the concave mirror , after refraction these rays will
converge at a point which is . between pole and focus of the lens if we consider
other, marginal rays we can see these will focus at some other points , so at various
points we can say all parallel rays will be meeting and we can say the focus will spreaded
between, few points not at a single point , but if we consider paraxial rays there will
be pin pointed sharp focus is obtained . so here we can say , for a given point object
point image is produced by a lens or a mirror- only when paraxial rays, incident from object
onto the optical device lens or mirror is considered if we consider marginal rays which
are incident on lens or mirror away from principal axis, the image produced will also be blurred
or distributed between few points . so here we can write a note that . due to
, spherical , aberrations. a lens – or a mirror . of large aperture . fails to produce .
sharp image . of an object – or. point image
. of a point object. and it is due to, marginal rays , so if a lens or mirror is having very
small aperture only paraxial rays will be refracted from the lens or mirror there will
be point image of point object or sharp image of object is produced . this is the phenomenon
we call spherical aberrations.

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